The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...) not trivialize in LDI's, several logical dependencies of classical logic are blocked in the context of LDI's, allowing to dissolve the paradox. (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian (...) and Brazilian schools’ objections. In the appendix of the paper, I also argue that the Brazilian school’s view of logic is not coherent. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.

We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is (...) based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ+ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not. (shrink)

In this paper a first order theory for the logics defined through literal paraconsistent-paracomplete matrices is developed. These logics are intended to model situations in which the ground level information may be contradictory or incomplete, but it is treated within a classical framework. This means that literal formulas, i.e. atomic formulas and their iterated negations, may behave poorly specially regarding their negations, but more complex formulas, i.e. formulas that include a binary connective are well behaved. This situation may and does (...) appear for instance in data bases. (shrink)

In his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that (...) Beall should consider another weaker subclassical logic as the logic adequate for his project. To this end, we first briefly present Beall’s argument for FDE. Then, we discuss two specific topics that seem to motivate us to weaken FDE. We then introduce a subsystem that will enjoy all the benefits of Beall’s suggestion. (shrink)

In the paper, we tackle the matter of non-classical logics, in particular, paraconsistent ones, for which not every formula follows in general from inconsistent premisses. Our benchmark is Jaśkowski’s logic, modeled with the help of discussion. The second key origin of this paper is the matter of being tabular, i.e. being adequately expressible by finitely many finite matrices. We analyse Jaśkowski’s non-tabular discussive (discursive) logic $ \textbf {D}_{2}$, one of the first paraconsistent logics, from the perspective of a trivalent tabular (...) logic. We are motivated to step down from the ongoing modal $ \textbf {S5}$-perspective of developing $ \textbf {D}_{2}$ both by certain mysteries that have been surrounding it and by gaps in Jaśkowski’s arguments contra the multivalent tabular perspective. Although Jaśkowski’s idea to use $ \textbf {S5}$ in order to define $ \textbf {D}_{2}$ is very attractive since it allows one to benefit from the tools and results of modal logic, it also gives a ‘non-direct’ formulation and, as it appeared later, is superfluous with respect to what is meant to be achieved since one can define the very same logic but using modal logics weaker than S5. It is also known, due to Kotas, that discussive logic is not finite-valued. So, in light of Kotas’s result that $ \textbf {D}_{2}$ is non-tabular, we propose to associate it with a few dozen discussive formulae that Jaśkowski unequivocally and illustratively suggests to be its theorems or non-theorems rather than with axioms of its modern axiomatizations (one of which Kotas employs) in order to be capable of performing a computer-aided brute-force search for suitable trivalent matrices in the cases of one and two designated values. As a result, we find trivalent matrices with two designated values that might be dubbed ‘discussive’ because they meet Jaśkowski’s suggestion to validate and invalidate the litmus theorems and non-theorems, respectively, despite the fact that none of them validates all the negation axioms in the modern axiomatizations of $ \textbf {D}_{2}$. The matrices found are then analysed along with highlighting the ones that were previously mentioned in the literature. We conclude the paper with a comparative analysis of Omori’s results and a test of Karpenko’s hypothesis. (shrink)